Similar to how a loop atom can be expressed on an RBM weight matrix as a rectangle, a frustrated loop of length 4 can be expressed also as a rectangle on the adjacency matrix [1]} of a general graph. To be more specific, the cycle \(i_1-i_2-i_3-i_4-i_1\)  can be expressed as a rectangle with indexes \((i_1,i_2)\) , \((i_2,i_3)\) , \((i_3,i_4)\) , and \((i_4,i_1)\) . Since the graph is not necessarily bipartite, the visible-hidden ordering of the coordinate indices is not well-defined, meaning that the rectangle is not unique. Alternatively, the rectangle can also be \((i_1,i_4)\) , \((i_4,i_3)\) , \((i_3,i_2)\) , and \((i_2,i_1)\) , which is simply the “transpose" of the first rectangle on the adjacency matrix. Therefore, to ensure the required symmetry of the adjacency matrix, we express the loop atom as the sum of the two rectangle representations.
